Clearly you are unfamiliar with the concept of an "analogy". An analogy is not meant to compare two situations in every possible way. Obviously baseball is not random, and PECOTA is not merely a bunch of averages. That isn't the point. I am not trivializing the difference between "weighted statistical models" and random events any more than I would be trivializing the difference between fish and mammals if I were to say sharks:teeth::whales:baleen. Obviously, These two animals are very different in many ways. The analogy would be pointing out nothing more than the fact that teeth and baleen are located in the same place on the animal's anatomy--AND NOTHING MORE. It does not imply that they serve the same purpose or that they are made of the same material (they don't, and they're not).

I realize that I've just used an analogy to explain the concept of analogies, but bear with me.

Likewise, my die analogy does not imply that PECOTA is nothing more than arithmetic means. I will spell it out for you again: The analogy is that in both the case of the die roll, and the case of executives who place a lot of weight on PECOTA projections, you have a person who is basing an important decision purely on numbers, where there are other factors at play. In the case of the die, the other factor is that 3.5 is not a number on a die. In the case of PECOTA, the other factors are various--managers, team chemistry, fan support, etc, etc.
In a way though, you did grasp my point--guessing 3.5 as a die roll is obviously absurdly stupid. I'm arguing that basing baseball decisions PURELY on numbers is also pretty damn stupid, if not as stupid as the former.

NO, YOUR ANALOGY JUST SUCKS, GUY. You obviously have no idea what you're talking about, the fact that you keep hammering on this ridiculous notion that someone who understands how stats and probability work would actually come up with 3.5 as the most likely number to come up on a 6-sided dice only goes to prove that. By your logic, I could say that the printed word is useless because look, if I pound away on my keyboard I get:

This is, of course, a completely invalid argument because anyone would note that if you don't follow the simple rules of grammar, spelling, etc. you will get jibberish. Likewise, if you don't follow the rules of basic stats and probability, you will get jibberish. But your worthless example that "3.5 is the most common number to come up on a 6-sided dice" doesn't invalidate stats and probability any more than my worthless keyboard pounding invalidates reading or writing. It just proves when you do stupid things, you get stupid answers.

And yes, comparing weighted models like PECOTA to random events, again, underscores that you do not have a solid grasp of these ideas. A person betting on which number a dice roll will come next can get no help from looking back at the last 10,000 times that dice was rolled. The next number up is a completely random event. But, much in the same way you probably think Paul Konerko will be a better hitter this season than Gordon Beckham or Tyler Flowers, PECOTA does take past results into consideration and likewise, will probably tell you Konerko is more likely to be successful hitting this season than Beckham or Flowers. It is a weighted model designed to take past results and make an educated guess, much like you when you watch the Sox and then look at their projected lineups and rosters on paper in February. Just because you disagree with the way PECOTA or any other model works does not mean they are just taking magic numbers out of the sky. There is an actual method to that mean. So to say it's the same thing as rolling a dice and getting 3.5 shows that you really have no idea what you're talking about.